David Cameron has marched onto territory staked out by Ed Miliband by promising that there would be no return to the "turbo-capitalism" of recent decades.

In the third new year intervention by the main party leaders on what is being described as "responsible capitalism", the prime minister revived a signature theme of his time in opposition when he said he would preside over an era of "popular capitalism".

"I want these difficult economic times to achieve more than just paying down the deficit and encouraging growth," he said. He also announced a co-operatives bill to give public sector workers a greater chance to create mutuals to deliver public services.

"I want them to lead to a socially responsible and genuinely popular capitalism," he said.

Miliband publicly welcomed the prime minister's decision to address issues he marked out in his Labour conference speech last year when he promised to champion "producer" businesses and to crack down on "predator" businesses. But in private, the Labour leader dismissed the speech as a "doughnut" – attractive on the outside, but with nothing in the middle.

In a parallel speech to the Which! consumer rights organisation, Miliband said: "I frankly don't believe that this prime minister is serious about this agenda. Why? He attacked me last year when I talked about irresponsible capitalism, and I'm afraid it's never going to work if your basic view is that government should just get out of the way."

The prime minister, whose pollsters say Miliband's ideas for forging a new form of capitalism are resonating with voters, challenged two Labour claims – that it is best placed to reform the free market and that the Tories are disqualified from contributing to the debate because they are the party of capital.

Cameron said New Labour was to blame for the excesses of recent years, adding: "Three years ago, I argued that the previous government's turbo-capitalism turned a blind eye to corporate excess while we believed in responsible capitalism and would make it happen.

"The last government claimed to have got rid of boom and bust. What it really did was allow a debt-fuelled boom to get out of control.

"The result was a series of lethal imbalances in our economy, between north and south, between financial services and manufacturing, between the people who got huge rewards at the top, or welfare at the bottom, while everyone else seemed to be left out. The truth is that the last government made a Faustian pact with the City."

He said the Tories had a record for promoting social responsibility that dated back to the era of Edmund Burke, who insisted on public accountability for the East India Company.

This spirit led to the Factory Acts under Benjamin Disraeli, which began to set working conditions, and continued into the modern era as Conservatives forged a "genuinely popular capitalism" by opening up markets, he said.

"A consistent Conservative theme has been the ambition of building a nation of shareholders, savers and homeowners," Cameron said. "Macmillan championed this through home ownership, giving people an asset of their own. Margaret Thatcher did the same with privatisation and share ownership."

The Conservative party had shown that progress was not achieved by abandoning the free market, which actually promoted morality, he said, adding: "I believe that open markets and free enterprise are the best imaginable force for improving human wealth and happiness. They are the engine of progress, generating the enterprise and innovation that lifts people out of poverty and gives people opportunity.

"I would go further: where they work properly, open markets and free enterprise can actually promote morality. Why? Because they create a direct link between contribution and reward, between effort and outcome. The fundamental basis of the market is the idea of something for something – an idea we need to encourage, not condemn. So we should use this crisis of capitalism to improve markets, not undermine them."

The prime minister said the Tories were best placed to reform the free market because the party understood its failing and strengths, unlike Labour which either promoted the economics of socialism or "let capitalism rip" under Tony Blair and Gordon Brown. "No true Conservative has a naive belief that all politics has to do is step back and let capitalism rip," he added.

Aides say Miliband is confident that Cameron will fail because he has no understanding of the difficulties many people are experiencing or the role the government should play in changing the rules. The Labour leader believes he will trump Cameron in three key areas:

• Changing the rules. Miliband wrote in the FT on Thursday about introducing new rules for takeovers to prevent a repeat of the "unedifying spectacle" of the Kraft takeover of Cadbury.

• Standing up for people suffering in the downturn. Miliband says his pledge to break up the big six energy companies is an example of this.

• Understanding that the world has utterly changed. "We are no longer in the politics of 'and' but are now into the politics of 'or'," one source said. "Tough choices will have to be made. But in Ed's case they will be informed by his values. David Cameron just thinks the government should get out of the way."